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Inventiones mathematicae

, Volume 188, Issue 3, pp 659–711 | Cite as

The isogeny conjecture for A-motives

  • Richard Pink
Article
  • 201 Downloads

Abstract

We prove the isogeny conjecture for A-motives over finitely generated fields K of transcendence degree ≤1. This conjecture says that for any semisimple A-motive M over K, there exist only finitely many isomorphism classes of A-motives M′ over K for which there exists a separable isogeny M′→M. The result is in precise analogy to known results for abelian varieties and for Drinfeld modules and will have strong consequences for the \({\mathfrak {p}}\)-adic and adelic Galois representations associated to M. The method makes essential use of the Harder–Narasimhan filtration for locally free coherent sheaves on an algebraic curve.

Keywords

Isomorphism Class Short Exact Sequence Abelian Variety Pole Order Coherent Sheaf 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© Springer-Verlag 2011

Authors and Affiliations

  1. 1.Department of MathematicsETH ZurichZurichSwitzerland

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